She travelled eight hours by bus for violin lessons. Now she's playing Wembley with Coldplay

Pathrycia Mendonça never has to worry about jet lag.

The 26-year-old has just jetted into London, where she's about to play 10 nights at Wembley Stadium with Coldplay as part of Venezuela's Simón Bolívar Symphony Orchestra.

The flight took 12 hours and meant leaving her beloved 10-month-old daughter at home with her mother – but the violinist is bursting with energy as she arrives for rehearsals at the iconic Air Studios in north London.

That's probably because, as a 12-year-old student in Venezuela, she endured long, overnight bus journeys just to attend her lessons in Caracas.

"I am from Barquisimeto, which is a small town, and it is eight hours on the bus, because it's so slow," she explains.

"So when I started my classes, I would leave Barquisimeto at midnight to arrive in Caracas at dawn.

"I'd go to my classes then, at midday, I'd go back to my city with my mum. She was always with me, because I was a child. And I'd do it every week.

"For me, that was the key to being part of the orchestra here, now."

In other words, sleep deprivation means nothing to her.

Speaking to Mendonça, you'd be forgiven for feeling inadequate. As well as her position in the world-famous orchestra, she is also a violin teacher, a mother and a chef, and recently completed a Master's degree in music.

But she wouldn't be anywhere else in the world for the next three weeks.

"I don't know if I can say this, but I'm a crazy fan of Coldplay, so when they said, 'Do you want to come and play?' I was like, 'No way!'" she laughs, sheepishly.

"When I listen to the band in my house, I always dreamt about playing Viva La Vida. It's so iconic, and it has strings all the way through. So this is a dream that came true. Totally a dream."

Like her fellow players in the Simón Bolívar Symphony Orchestra, Mendonça is a beneficiary of Venezuela's El Sistema programme, which offers free music education throughout the country.

It was established in 1975 by visionary musician José Antonio Abreu, who saw it as an antidote to the crime and poverty that gripped the nation.

Those problems persist despite the country's vast oil wealth – but El Sistema ("the system") has earned Venezuela's musicians a place on the world stage.

To the players, it's about more than learning an instrument.

"El Sistema teaches you about the discipline of the community," says Humberto Jiminez, a violinist who also made weekly six-hour journeys to Caracas for his studies.

"You have to learn when to be part of the team, and when to be a leader – and how to integrate all those differences into one intention."

"It gave me everything," adds Mendonça. "My whole life, I think. It gives me motivation."

El Sistema's most famous graduate is Gustavo Dudamel, a seven-time Grammy winner who has been called "the happiest conductor in America" and "the closest thing to a rock star" in the world of classical music.

The 44-year-old is currently musical director of the Los Angeles Philharmonic and artistic director of the Simón Bolívar Orchestra. Next year, he will become the first Latin American to lead the New York Philharmonic, the oldest symphony orchestra in the US.

But for the next three weeks, he's in London too – summoned by Chris Martin to open every night of Coldplay's record-breaking residency at Wembley Stadium.

"Chris is very into social action through music," says Dudamel. "When he plays music, his will is to help, to heal and to transform - and that connects with our values.

"I think he wanted to give something to the orchestra. A gift, a very generous gift, of having all of us together, celebrating the power of music."

Their partnership fits perfectly with Dudamel's urge to push the boundaries of classical music.

Earlier this year, he took the LA Philharmonic to the Coachella Music Festival, playing Wagner and Beethoven in a 50-minute set that also included guest stars such as Dave Grohl, Cynthia Erivo and LL Cool J.

"You think, 'Maybe this is something crazy', but it was the most natural thing," he says, recalling the way the audience chanted the opening "da-da-da-dum" of Beethoven's 5th like it was the riff from Seven Nation Army.

"We live in a world of walls and borders - and that happens with music, too," says Dudamel. "But it's been one of my goals to break that down.

"I think young people are hungry for culture and for us, in the orchestra, [Coachella] was a historical moment of embracing another audience and that audience connecting with what we do."

He's hopeful the Wembley shows – where the orchestra will again play Beethoven's 5th, alongside John Williams' Star Wars theme and Vivaldi's Spring – will have the same effect.

"I want the audience to walk away embraced by love," he says.

"It's not naïve to say we're living in a crisis of empathy. Music is not about that. Music is about making harmony together. It's the best example of how to behave as a community."

The conductor's optimism is infectious. As he leads the orchestra in rehearsals at London's Air Studios, they whoop and cheer, enjoying themselves in a way that orchestras rarely do.

It's proof of El Sistema's importance, as it turns 50 – an anniversary that's being marked with a mini-residency at London's Barbican, and a new album, called Odyssey, that mixes Latin American traditions with orchestral music.

But the organisation has come in for criticism. Some have accused it of being a political organisation, pointing out that it sits under the office of president Nicolás Maduro – who has repeatedly been accused of repressing opposition groups and silencing dissent, including with the use of violence.

Dudamel has criticised Maduro, calling for an end to "bloodshed" after an 18-year-old musician was killed at a protest in Caracas. But some have called for him to go further, saying his continued involvement with El Sistema makes him the president's "puppet and henchman".

But the conductor says his priority will always be the children whose lives are transformed by the programme.

"In the super-politicised world that we live in right now, you have to say, you have to do, you have be against.

"It's difficult because everybody is screaming – but we need more of these programmes that motivate you to find the best of people.

"For me, the most important thing is that this new generation has the opportunities that I had."

More than three million children have passed through El Sistema over the last five decades, with the programme replicated in dozens of countries around the world.

Over the next three weeks, almost one million people will see the results on stage at Wembley.

"It's the biggest number of people that I ever played. It's a lot," marvels Mendonça.

"It's a way to represent my country and, in my particular case, it's a way to give hope to all the children I've had the opportunity to teach.

"Sometimes, when you're growing up, you don't know why you are doing the things you do... But when you see someone close to you doing something like this, you say, 'If she can, why can't I?'"